a) The mean distance cycled is estimated to be 94 km. b) The median lies in the class 100 km < d < 150 km.
a) Calculating the Mean
To estimate the mean distance cycled, we need to find the sum of all the distances and divide it by the total frequency. Using the given table:
0 km: Frequency = 4
50 km: Frequency = 10
100 km < d < 150 km: Frequency = 2
150 km: Frequency = 9
To find the sum, multiply each distance by its frequency and then add them up:
0 km * 4 = 0
50 km * 10 = 500
2 * [(100 + 150)/2] = 500
150 km * 9 = 1350
Sum = 0 + 500 + 500 + 1350 = 2350 km
To find the mean, divide the sum by the total frequency:
Mean = Sum / Total Frequency = 2350 km / (4 + 10 + 2 + 9) = 2350 km / 25 = 94 km
b) Locating the Median
To find the class in which the median lies, we need to arrange the distances in ascending order. The distances are: 0 km, 50 km, 100-150 km, 150 km.
The median is the middle value when the distances are arranged in order. Since the frequency of the 100-150 km class is 2, the median lies in this class. Therefore, the median lies in the class 100 km < d < 150 km.
The probable question may be:
How did you determine the class in which the median lies?
Why is the median located in the class 100 km < d < 150 km?